As is known, in many countries, the regulations governing atmospheric pollution are becoming increasingly strict with regard to the composition of internal combustion engine exhaust gas.
In the case of diesel engines in particular, the main problems are posed not so much by carbon monoxide (CO) and hydrocarbons (HC) as by nitric oxides (NOx) and particulate in the exhaust gas.
Various sources have shown that even modern direct-injection diesel engines introduced onto the market at the end of the 90s are characterized by serious particulate emissions.
Numerous methods have been proposed whereby to minimize the particulate content of exhaust gas emitted into the atmosphere. Of these, fitting the exhaust pipe with a particulate filter has long been acknowledged in engine technology as undoubtedly the final solution to the problem of diesel engine particulate emissions.
A particulate filter—also known as particulate trap (soot catcher or soot trap)—normally comprises a number of parallel, porous-walled, alternately obstructed channels.
More specifically, the obstructions force the exhaust gas to flow through the lateral walls of the channels, so that the unburned particles constituting the particulate are first retained in the pores of the lateral walls, and, when the pores eventually become clogged, accumulate and form a porous layer on the inner surfaces of the channel walls.
As the particulate accumulates on the inner surfaces of the channel walls, the pressure drop through the filter, and therefore the backpressure generated by the filter, also increases.
If not removed eventually, an excessive accumulation of particulate therefore results in:                impaired performance, driving comfort, and consumption of the engine, until the engine eventually stalls; and        destruction of the filter itself in the event of self-firing and uncontrolled combustion of the particulate. In particular driving conditions, a large accumulation of particulate may give rise to “critical” regeneration phenomena consisting in sudden, uncontrolled particulate combustion, thus resulting in overheating of the ceramic matrix of the filter and in possible damage to the filter itself.        
The trapped particulate must therefore be removed regularly by regenerating the particulate filter, which, in engine technology, means burning the accumulated particulate (mainly composed of carbon, C) which, in contact with the oxygen in the exhaust gas, is converted into carbon monoxide CO and carbon dioxide CO2.
This reaction, however, only occurs spontaneously (i.e. without using additives) at temperatures over roughly 600° C., which are much higher than those at the filter inlet in normal engine operating conditions.
In certain conditions, i.e. on detecting a given accumulation of particulate in the filter, the exhaust gas temperature at the filter inlet must therefore be increased artificially to initiate particulate combustion.
Numerous methods of artificially increasing exhaust gas temperature at the filter inlet to initiate particulate combustion have been proposed and/or actually implemented.
One of the main drawbacks of current on-vehicle particulate combustion initiation methods lies in regeneration of the particulate filter being initiated cyclically on the basis of mileage, e.g. every 500 or 1000 km, independently of the actual amount of particulate accumulated in the filter.
Mileage-based particulate filter regeneration has recently been proved beyond all doubt to be totally inefficient, by frequently initiating regeneration of the filter unnecessarily, or conversely, by not initiating regeneration of the filter even when actually required.
Tests have shown particulate accumulation in the filter does not depend solely on mileage, but is also fairly seriously affected by other factors, such as vehicle mission profile (e.g. urban or highway driving) and driving style (e.g. sport oriented). Moreover, any engine imperfections, which may result in a considerable increase in particulate emissions, are not taken into account; in which case, particulate may accumulate in the filter to the extent of seriously impairing engine and filter reliability.
To accurately determine the amount of particulate accumulated in the filter, so as to only initiate regeneration of the filter when the amount exceeds given levels, various authors have proposed numerous physical models by which to calculate the mass of accumulated particulate on the basis of exhaust gas flow and temperature and the pressure drop through the filter. All the models proposed are substantially based on the assumption that particulate distribution inside the filter channels and the physical-chemical properties of the particulate remain even and constant, independently of variations in the operating condition of the engine and in past particulate accumulation.
For example, in Konstandopoulos A. G., Kostoglou M., Skaperdas E., Papaioannou E., Zarvalis D., and Kladopoulou E., “Fundamental Studies of Diesel Particulate Filters: Transient Loading, Regeneration and Ageing”, SAE 2000-01-1016, 2000, assuming even (axial and radial) spatial particulate distribution inside the channels, an analytical particulate filter model is proposed which takes into account various factors, such as filter geometry, physical characteristics of the filter material, particulate characteristics, etc., which are assumed constant, independently of variations in the operating condition of the engine and in past particulate accumulation.
For the sake of clarity, the following is the complete equation (eq. 1) developed by the Applicant from the considerations made in the above publication as a model of the particulate filter, possibly with a catalytic converter upstream from the filter:                                                                         Δ                ⁢                                                                   ⁢                                                      P                    DPF                                    ⁡                                      (                                                                                            Δ                          ⁢                                                                                                           ⁢                                                      P                            DPF                                                                          2                                            +                                              P                                                  a                          ⁢                                                                                                           ⁢                          t                          ⁢                                                                                                           ⁢                          m                                                                                      )                                                              =                            ⁢                                                                                          μ                      o                                        ⁢                                          T                                              δ                        +                        1                                                              ⁢                    R                                                        2                    ⁢                                                                                   ⁢                                          M                      w                                                                      ⁢                                  Q                  m                                ⁢                                                                                                    (                                                  H                          +                          w                                                )                                            2                                                              V                      trap                                                        ·                                                                                                                      ⁢                              [                                                      w                                                                  k                        m                                            ⁢                      H                                                        -                                                            1                                              4                        ⁢                                                  k                          s                                                                                      ⁢                                          ln                      ⁡                                              (                                                  1                          -                                                                                                                    m                                s                                                                                            ρ                                s                                                                                      ·                                                          1                                                              NLH                                2                                                                                                                                    )                                                                              +                                                                                                                                        ⁢                                                                            4                      3                                        ⁢                                                                  FL                        2                                                                    H                        4                                                                              +                                                            4                      3                                        ⁢                                                                  FL                        2                                                                    H                        4                                                              ⁢                                                                  (                                                  1                          -                                                                                                                    m                                s                                                                                            ρ                                s                                                                                      ·                                                          1                                                              NLH                                2                                                                                                                                    )                                                                    -                        2                                                                                            ]                            +                                                                                        ⁢                                                                    TR                                          M                      w                                                        ⁢                                      Q                    m                    2                                    ⁢                                                                                                              (                                                      H                            +                            w                                                    )                                                4                                                                                              H                          2                                                ⁢                                                  V                          trap                          2                                                                                      ⁡                                          [                                                                        w                                                      4                            ⁢                                                          k                              m                              ′                                                                                                      +                                                  2                          ⁢                                                                                                           ⁢                                                                                    ξ                              ⁡                                                              (                                                                  L                                  H                                                                )                                                                                      2                                                                                              ]                                                                      +                                                                                                      ⁢                                                                                          μ                      o                                        ⁢                                          T                                              δ                        +                        1                                                              ⁢                    R                                                        2                    ⁢                                          M                      w                                                                      ⁢                                  Q                  m                                ⁢                                                                                                    (                                                                              H                            cat                                                    +                                                      w                            cat                                                                          )                                            2                                                              V                      cat                                                        ⁡                                      [                                                                  4                        3                                            ⁢                                                                        FL                          cat                          2                                                                          H                          cat                          4                                                                                      ]                                                                                                          (                  eq          .                                           ⁢          1                )            where:    Vtrap,H,L,N,w are the following geometric properties of the filter: volume, cell size, length, number of open cells, wall thickness;    km,k′m are the following properties of the filter material: linear and nonlinear permeability;    Vcat,Hcat,Lcat,Wcat are the following geometric properties of the catalyst: volume, cell size, length, wall thickness;    R,F,ξ are the following constants: gas constant (8.314 J/(K·mol)), gas friction coefficient in square-section conduits (˜28.454), inertial term (˜3);    Patm,Mw,T,μo are the following exhaust gas properties: absolute pressure downstream from the filter (may be considered roughly equal to atmospheric pressure), gas mean molecular weight, temperature, viscosity factor;    ms,ks,ρs are the following physical-chemical particulate properties: mass, permeability, density; and    ΔPDPF,Qm are the total pressure drop across the filter and mass exhaust gas flow.
Implementing the above equation at engine control unit level to determine the particulate mass mS accumulated in the filter would be particularly complex, in that defining and calculating the particulate mass mS as a function of the other variables involved would call for computing power far beyond that of currently used automotive engine control units.
Even if the equation could be implemented in the engine control unit, the results would be totally unsatisfactory. Bench and on-vehicle tests conducted by the Applicant, in fact, have shown that assuming even, constant particulate distribution in the filter channels and constant physical-chemical properties of the particulate, independently of variations in the operating condition of the engine and in past particulate accumulation, makes it impossible to obtain a correct estimate of the amount of particulate accumulated in the filter in real operating conditions. Which is why regeneration control systems based on measuring exhaust gas flow and temperature and the pressure drop across the filter have never be employed in the automotive industry.